%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : NUM569+3 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% Computer : n019.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri Sep 25 02:26:03 PM UTC 2026
% Result : Theorem 80.58s 18.53s
% Output : CNFRefutation 80.58s
% Verified :
% SZS Type : ERROR: Analysing output (Could not find formula named f215ERROR: Could not build tree for root c_92014ERROR: MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [X0] :
( aSet0(X0)
=> ! [X1] :
( aElementOf0(X1,X0)
=> aElement0(X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mEOfElem) ).
fof(f10,axiom,
! [X0] :
( aSet0(X0)
=> ! [X1] :
( aSubsetOf0(X1,X0)
<=> ( ! [X2] :
( aElementOf0(X2,X1)
=> aElementOf0(X2,X0) )
& aSet0(X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefSub) ).
fof(f16,axiom,
! [X0,X1] :
( ( aElement0(X1)
& aSet0(X0) )
=> ! [X2] :
( X2 = sdtmndt0(X0,X1)
<=> ( ! [X3] :
( aElementOf0(X3,X2)
<=> ( X3 != X1
& aElementOf0(X3,X0)
& aElement0(X3) ) )
& aSet0(X2) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefDiff) ).
fof(f24,axiom,
aElementOf0(sz00,szNzAzT0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mZeroNum) ).
fof(f25,axiom,
! [X0] :
( aElementOf0(X0,szNzAzT0)
=> ( szszuzczcdt0(X0) != sz00
& aElementOf0(szszuzczcdt0(X0),szNzAzT0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSuccNum) ).
fof(f27,axiom,
! [X0] :
( aElementOf0(X0,szNzAzT0)
=> ( ? [X1] :
( X0 = szszuzczcdt0(X1)
& aElementOf0(X1,szNzAzT0) )
| X0 = sz00 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mNatExtra) ).
fof(f30,axiom,
! [X0] :
( aElementOf0(X0,szNzAzT0)
=> sdtlseqdt0(sz00,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mZeroLess) ).
fof(f35,axiom,
! [X0,X1] :
( ( aElementOf0(X1,szNzAzT0)
& aElementOf0(X0,szNzAzT0) )
=> ( ( sdtlseqdt0(X1,X0)
& sdtlseqdt0(X0,X1) )
=> X0 = X1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mLessASymm) ).
fof(f39,axiom,
! [X0] :
( aElementOf0(X0,szNzAzT0)
=> iLess0(X0,szszuzczcdt0(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mIH) ).
fof(f50,axiom,
! [X0] :
( aElementOf0(X0,szNzAzT0)
=> ! [X1] :
( X1 = slbdtrb0(X0)
<=> ( ! [X2] :
( aElementOf0(X2,X1)
<=> ( sdtlseqdt0(szszuzczcdt0(X2),X0)
& aElementOf0(X2,szNzAzT0) ) )
& aSet0(X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefSeg) ).
fof(f75,axiom,
( isCountable0(xS)
& aSubsetOf0(xS,szNzAzT0)
& ! [X0] :
( aElementOf0(X0,xS)
=> aElementOf0(X0,szNzAzT0) )
& aSet0(xS) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__3435) ).
fof(f82,conjecture,
! [X0] :
( aElementOf0(X0,szNzAzT0)
=> ( ! [X1] :
( aElementOf0(X1,szNzAzT0)
=> ( iLess0(X1,X0)
=> ( isCountable0(sdtlpdtrp0(xN,X1))
& aSubsetOf0(sdtlpdtrp0(xN,X1),szNzAzT0)
& ! [X2] :
( aElementOf0(X2,sdtlpdtrp0(xN,X1))
=> aElementOf0(X2,szNzAzT0) )
& aSet0(sdtlpdtrp0(xN,X1)) ) ) )
=> ( isCountable0(sdtlpdtrp0(xN,X0))
& ( aSubsetOf0(sdtlpdtrp0(xN,X0),szNzAzT0)
| ( ! [X1] :
( aElementOf0(X1,sdtlpdtrp0(xN,X0))
=> aElementOf0(X1,szNzAzT0) )
& aSet0(sdtlpdtrp0(xN,X0)) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(f83,negated_conjecture,
~ ! [X0] :
( aElementOf0(X0,szNzAzT0)
=> ( ! [X1] :
( aElementOf0(X1,szNzAzT0)
=> ( iLess0(X1,X0)
=> ( isCountable0(sdtlpdtrp0(xN,X1))
& aSubsetOf0(sdtlpdtrp0(xN,X1),szNzAzT0)
& ! [X2] :
( aElementOf0(X2,sdtlpdtrp0(xN,X1))
=> aElementOf0(X2,szNzAzT0) )
& aSet0(sdtlpdtrp0(xN,X1)) ) ) )
=> ( isCountable0(sdtlpdtrp0(xN,X0))
& ( aSubsetOf0(sdtlpdtrp0(xN,X0),szNzAzT0)
| ( ! [X1] :
( aElementOf0(X1,sdtlpdtrp0(xN,X0))
=> aElementOf0(X1,szNzAzT0) )
& aSet0(sdtlpdtrp0(xN,X0)) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f82]) ).
fof(f94,plain,
~ ! [X0] :
( aElementOf0(X0,szNzAzT0)
=> ( ! [X1] :
( aElementOf0(X1,szNzAzT0)
=> ( iLess0(X1,X0)
=> ( isCountable0(sdtlpdtrp0(xN,X1))
& aSubsetOf0(sdtlpdtrp0(xN,X1),szNzAzT0)
& ! [X2] :
( aElementOf0(X2,sdtlpdtrp0(xN,X1))
=> aElementOf0(X2,szNzAzT0) )
& aSet0(sdtlpdtrp0(xN,X1)) ) ) )
=> ( isCountable0(sdtlpdtrp0(xN,X0))
& ( aSubsetOf0(sdtlpdtrp0(xN,X0),szNzAzT0)
| ( ! [X3] :
( aElementOf0(X3,sdtlpdtrp0(xN,X0))
=> aElementOf0(X3,szNzAzT0) )
& aSet0(sdtlpdtrp0(xN,X0)) ) ) ) ) ),
inference(rectify,[],[f83]) ).
fof(f95,plain,
! [X0] :
( ~ aSet0(X0)
| ! [X1] :
( ~ aElementOf0(X1,X0)
| aElement0(X1) ) ),
inference(ennf_transformation,[],[f3]) ).
fof(f101,plain,
! [X0] :
( ~ aSet0(X0)
| ! [X1] :
( aSubsetOf0(X1,X0)
<=> ( ! [X2] :
( ~ aElementOf0(X2,X1)
| aElementOf0(X2,X0) )
& aSet0(X1) ) ) ),
inference(ennf_transformation,[],[f10]) ).
fof(f111,plain,
! [X0,X1] :
( ~ aElement0(X1)
| ~ aSet0(X0)
| ! [X2] :
( X2 = sdtmndt0(X0,X1)
<=> ( ! [X3] :
( aElementOf0(X3,X2)
<=> ( X3 != X1
& aElementOf0(X3,X0)
& aElement0(X3) ) )
& aSet0(X2) ) ) ),
inference(ennf_transformation,[],[f16]) ).
fof(f112,plain,
! [X0,X1] :
( ~ aElement0(X1)
| ~ aSet0(X0)
| ! [X2] :
( X2 = sdtmndt0(X0,X1)
<=> ( ! [X3] :
( aElementOf0(X3,X2)
<=> ( X3 != X1
& aElementOf0(X3,X0)
& aElement0(X3) ) )
& aSet0(X2) ) ) ),
inference(flattening,[],[f111]) ).
fof(f124,plain,
! [X0] :
( ~ aElementOf0(X0,szNzAzT0)
| ( szszuzczcdt0(X0) != sz00
& aElementOf0(szszuzczcdt0(X0),szNzAzT0) ) ),
inference(ennf_transformation,[],[f25]) ).
fof(f127,plain,
! [X0] :
( ~ aElementOf0(X0,szNzAzT0)
| ? [X1] :
( X0 = szszuzczcdt0(X1)
& aElementOf0(X1,szNzAzT0) )
| X0 = sz00 ),
inference(ennf_transformation,[],[f27]) ).
fof(f128,plain,
! [X0] :
( ~ aElementOf0(X0,szNzAzT0)
| ? [X1] :
( X0 = szszuzczcdt0(X1)
& aElementOf0(X1,szNzAzT0) )
| X0 = sz00 ),
inference(flattening,[],[f127]) ).
fof(f130,plain,
! [X0] :
( ~ aElementOf0(X0,szNzAzT0)
| sdtlseqdt0(sz00,X0) ),
inference(ennf_transformation,[],[f30]) ).
fof(f136,plain,
! [X0,X1] :
( ~ aElementOf0(X1,szNzAzT0)
| ~ aElementOf0(X0,szNzAzT0)
| ~ sdtlseqdt0(X1,X0)
| ~ sdtlseqdt0(X0,X1)
| X0 = X1 ),
inference(ennf_transformation,[],[f35]) ).
fof(f137,plain,
! [X0,X1] :
( ~ aElementOf0(X1,szNzAzT0)
| ~ aElementOf0(X0,szNzAzT0)
| ~ sdtlseqdt0(X1,X0)
| ~ sdtlseqdt0(X0,X1)
| X0 = X1 ),
inference(flattening,[],[f136]) ).
fof(f142,plain,
! [X0] :
( ~ aElementOf0(X0,szNzAzT0)
| iLess0(X0,szszuzczcdt0(X0)) ),
inference(ennf_transformation,[],[f39]) ).
fof(f160,plain,
! [X0] :
( ~ aElementOf0(X0,szNzAzT0)
| ! [X1] :
( X1 = slbdtrb0(X0)
<=> ( ! [X2] :
( aElementOf0(X2,X1)
<=> ( sdtlseqdt0(szszuzczcdt0(X2),X0)
& aElementOf0(X2,szNzAzT0) ) )
& aSet0(X1) ) ) ),
inference(ennf_transformation,[],[f50]) ).
fof(f194,plain,
( isCountable0(xS)
& aSubsetOf0(xS,szNzAzT0)
& ! [X0] :
( ~ aElementOf0(X0,xS)
| aElementOf0(X0,szNzAzT0) )
& aSet0(xS) ),
inference(ennf_transformation,[],[f75]) ).
fof(f201,plain,
? [X0] :
( aElementOf0(X0,szNzAzT0)
& ! [X1] :
( ~ aElementOf0(X1,szNzAzT0)
| ~ iLess0(X1,X0)
| ( isCountable0(sdtlpdtrp0(xN,X1))
& aSubsetOf0(sdtlpdtrp0(xN,X1),szNzAzT0)
& ! [X2] :
( ~ aElementOf0(X2,sdtlpdtrp0(xN,X1))
| aElementOf0(X2,szNzAzT0) )
& aSet0(sdtlpdtrp0(xN,X1)) ) )
& ( ~ isCountable0(sdtlpdtrp0(xN,X0))
| ( ~ aSubsetOf0(sdtlpdtrp0(xN,X0),szNzAzT0)
& ( ? [X3] :
( aElementOf0(X3,sdtlpdtrp0(xN,X0))
& ~ aElementOf0(X3,szNzAzT0) )
| ~ aSet0(sdtlpdtrp0(xN,X0)) ) ) ) ),
inference(ennf_transformation,[],[f94]) ).
fof(f202,plain,
? [X0] :
( aElementOf0(X0,szNzAzT0)
& ! [X1] :
( ~ aElementOf0(X1,szNzAzT0)
| ~ iLess0(X1,X0)
| ( isCountable0(sdtlpdtrp0(xN,X1))
& aSubsetOf0(sdtlpdtrp0(xN,X1),szNzAzT0)
& ! [X2] :
( ~ aElementOf0(X2,sdtlpdtrp0(xN,X1))
| aElementOf0(X2,szNzAzT0) )
& aSet0(sdtlpdtrp0(xN,X1)) ) )
& ( ~ isCountable0(sdtlpdtrp0(xN,X0))
| ( ~ aSubsetOf0(sdtlpdtrp0(xN,X0),szNzAzT0)
& ( ? [X3] :
( aElementOf0(X3,sdtlpdtrp0(xN,X0))
& ~ aElementOf0(X3,szNzAzT0) )
| ~ aSet0(sdtlpdtrp0(xN,X0)) ) ) ) ),
inference(flattening,[],[f201]) ).
fof(f221,plain,
! [X0] :
( ~ aSet0(X0)
| ! [X1] :
( ( ~ aSubsetOf0(X1,X0)
| ( ! [X2] :
( ~ aElementOf0(X2,X1)
| aElementOf0(X2,X0) )
& aSet0(X1) ) )
& ( ? [X2] :
( aElementOf0(X2,X1)
& ~ aElementOf0(X2,X0) )
| ~ aSet0(X1)
| aSubsetOf0(X1,X0) ) ) ),
inference(nnf_transformation,[],[f101]) ).
fof(f222,plain,
! [X0] :
( ~ aSet0(X0)
| ! [X1] :
( ( ~ aSubsetOf0(X1,X0)
| ( ! [X2] :
( ~ aElementOf0(X2,X1)
| aElementOf0(X2,X0) )
& aSet0(X1) ) )
& ( ? [X2] :
( aElementOf0(X2,X1)
& ~ aElementOf0(X2,X0) )
| ~ aSet0(X1)
| aSubsetOf0(X1,X0) ) ) ),
inference(flattening,[],[f221]) ).
fof(f223,plain,
! [X0] :
( ~ aSet0(X0)
| ! [X1] :
( ( ~ aSubsetOf0(X1,X0)
| ( ! [X3] :
( ~ aElementOf0(X3,X1)
| aElementOf0(X3,X0) )
& aSet0(X1) ) )
& ( ? [X2] :
( aElementOf0(X2,X1)
& ~ aElementOf0(X2,X0) )
| ~ aSet0(X1)
| aSubsetOf0(X1,X0) ) ) ),
inference(rectify,[],[f222]) ).
fof(f224,plain,
! [X0] :
( ~ aSet0(X0)
| ! [X1] :
( ( ~ aSubsetOf0(X1,X0)
| ( ! [X3] :
( ~ aElementOf0(X3,X1)
| aElementOf0(X3,X0) )
& aSet0(X1) ) )
& ( ( aElementOf0(sK11(X0,X1),X1)
& ~ aElementOf0(sK11(X0,X1),X0) )
| ~ aSet0(X1)
| aSubsetOf0(X1,X0) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK11]),skolemize(X2,sK11(X0,X1))],[f223]) ).
fof(f231,plain,
! [X1,X0] :
( ~ sP3(X1,X0)
| ! [X2] :
( ( sdtmndt0(X0,X1) != X2
| sP2(X2,X0,X1) )
& ( ~ sP2(X2,X0,X1)
| X2 = sdtmndt0(X0,X1) ) ) ),
inference(nnf_transformation,[],[f207]) ).
fof(f232,plain,
! [X0,X1] :
( ~ sP3(X0,X1)
| ! [X2] :
( ( sdtmndt0(X1,X0) != X2
| sP2(X2,X1,X0) )
& ( ~ sP2(X2,X1,X0)
| sdtmndt0(X1,X0) = X2 ) ) ),
inference(rectify,[],[f231]) ).
fof(f237,plain,
! [X0] :
( ~ aElementOf0(X0,szNzAzT0)
| ( szszuzczcdt0(sK14(X0)) = X0
& aElementOf0(sK14(X0),szNzAzT0) )
| X0 = sz00 ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK14]),skolemize(X1,sK14(X0))],[f128]) ).
fof(f250,plain,
! [X0] :
( ~ aElementOf0(X0,szNzAzT0)
| ! [X1] :
( ( slbdtrb0(X0) != X1
| ( ! [X2] :
( ( ~ aElementOf0(X2,X1)
| ( sdtlseqdt0(szszuzczcdt0(X2),X0)
& aElementOf0(X2,szNzAzT0) ) )
& ( ~ sdtlseqdt0(szszuzczcdt0(X2),X0)
| ~ aElementOf0(X2,szNzAzT0)
| aElementOf0(X2,X1) ) )
& aSet0(X1) ) )
& ( ? [X2] :
( ( aElementOf0(X2,X1)
| ( sdtlseqdt0(szszuzczcdt0(X2),X0)
& aElementOf0(X2,szNzAzT0) ) )
& ( ~ aElementOf0(X2,X1)
| ~ sdtlseqdt0(szszuzczcdt0(X2),X0)
| ~ aElementOf0(X2,szNzAzT0) ) )
| ~ aSet0(X1)
| X1 = slbdtrb0(X0) ) ) ),
inference(nnf_transformation,[],[f160]) ).
fof(f251,plain,
! [X0] :
( ~ aElementOf0(X0,szNzAzT0)
| ! [X1] :
( ( slbdtrb0(X0) != X1
| ( ! [X2] :
( ( ~ aElementOf0(X2,X1)
| ( sdtlseqdt0(szszuzczcdt0(X2),X0)
& aElementOf0(X2,szNzAzT0) ) )
& ( ~ sdtlseqdt0(szszuzczcdt0(X2),X0)
| ~ aElementOf0(X2,szNzAzT0)
| aElementOf0(X2,X1) ) )
& aSet0(X1) ) )
& ( ? [X2] :
( ( aElementOf0(X2,X1)
| ( sdtlseqdt0(szszuzczcdt0(X2),X0)
& aElementOf0(X2,szNzAzT0) ) )
& ( ~ aElementOf0(X2,X1)
| ~ sdtlseqdt0(szszuzczcdt0(X2),X0)
| ~ aElementOf0(X2,szNzAzT0) ) )
| ~ aSet0(X1)
| X1 = slbdtrb0(X0) ) ) ),
inference(flattening,[],[f250]) ).
fof(f252,plain,
! [X0] :
( ~ aElementOf0(X0,szNzAzT0)
| ! [X1] :
( ( slbdtrb0(X0) != X1
| ( ! [X3] :
( ( ~ aElementOf0(X3,X1)
| ( sdtlseqdt0(szszuzczcdt0(X3),X0)
& aElementOf0(X3,szNzAzT0) ) )
& ( ~ sdtlseqdt0(szszuzczcdt0(X3),X0)
| ~ aElementOf0(X3,szNzAzT0)
| aElementOf0(X3,X1) ) )
& aSet0(X1) ) )
& ( ? [X2] :
( ( aElementOf0(X2,X1)
| ( sdtlseqdt0(szszuzczcdt0(X2),X0)
& aElementOf0(X2,szNzAzT0) ) )
& ( ~ aElementOf0(X2,X1)
| ~ sdtlseqdt0(szszuzczcdt0(X2),X0)
| ~ aElementOf0(X2,szNzAzT0) ) )
| ~ aSet0(X1)
| X1 = slbdtrb0(X0) ) ) ),
inference(rectify,[],[f251]) ).
fof(f253,plain,
! [X0] :
( ~ aElementOf0(X0,szNzAzT0)
| ! [X1] :
( ( slbdtrb0(X0) != X1
| ( ! [X3] :
( ( ~ aElementOf0(X3,X1)
| ( sdtlseqdt0(szszuzczcdt0(X3),X0)
& aElementOf0(X3,szNzAzT0) ) )
& ( ~ sdtlseqdt0(szszuzczcdt0(X3),X0)
| ~ aElementOf0(X3,szNzAzT0)
| aElementOf0(X3,X1) ) )
& aSet0(X1) ) )
& ( ( ( aElementOf0(sK18(X0,X1),X1)
| ( sdtlseqdt0(szszuzczcdt0(sK18(X0,X1)),X0)
& aElementOf0(sK18(X0,X1),szNzAzT0) ) )
& ( ~ aElementOf0(sK18(X0,X1),X1)
| ~ sdtlseqdt0(szszuzczcdt0(sK18(X0,X1)),X0)
| ~ aElementOf0(sK18(X0,X1),szNzAzT0) ) )
| ~ aSet0(X1)
| X1 = slbdtrb0(X0) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK18]),skolemize(X2,sK18(X0,X1))],[f252]) ).
fof(f292,plain,
! [X0] :
( ~ sP9(X0)
| ( isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(X0)))
& aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(X0)),sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
& ! [X4] :
( ~ aElementOf0(X4,sdtlpdtrp0(xN,szszuzczcdt0(X0)))
| aElementOf0(X4,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0)))) )
& aSet0(sdtlpdtrp0(xN,szszuzczcdt0(X0)))
& sP8(X0)
& aSet0(sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
& ! [X2] :
( ~ aElementOf0(X2,sdtlpdtrp0(xN,X0))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,X0)),X2) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,X0)),sdtlpdtrp0(xN,X0)) ) ),
inference(nnf_transformation,[],[f215]) ).
fof(f293,plain,
! [X0] :
( ~ sP9(X0)
| ( isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(X0)))
& aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(X0)),sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
& ! [X2] :
( ~ aElementOf0(X2,sdtlpdtrp0(xN,szszuzczcdt0(X0)))
| aElementOf0(X2,sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0)))) )
& aSet0(sdtlpdtrp0(xN,szszuzczcdt0(X0)))
& sP8(X0)
& aSet0(sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
& ! [X1] :
( ~ aElementOf0(X1,sdtlpdtrp0(xN,X0))
| sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN,X0)),X1) )
& aElementOf0(szmzizndt0(sdtlpdtrp0(xN,X0)),sdtlpdtrp0(xN,X0)) ) ),
inference(rectify,[],[f292]) ).
fof(f297,plain,
( ! [X0] :
( ~ aElementOf0(X0,szNzAzT0)
| ~ isCountable0(sdtlpdtrp0(xN,X0))
| ( ~ aSubsetOf0(sdtlpdtrp0(xN,X0),szNzAzT0)
& ( ( aElementOf0(sK39(X0),sdtlpdtrp0(xN,X0))
& ~ aElementOf0(sK39(X0),szNzAzT0) )
| ~ aSet0(sdtlpdtrp0(xN,X0)) ) )
| sP9(X0) )
& sdtlpdtrp0(xN,sz00) = xS
& szDzozmdt0(xN) = szNzAzT0
& aFunction0(xN) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK39]),skolemize(X1,sK39(X0))],[f216]) ).
fof(f298,plain,
? [X0] :
( aElementOf0(X0,szNzAzT0)
& ! [X2] :
( ~ aElementOf0(X2,szNzAzT0)
| ~ iLess0(X2,X0)
| ( isCountable0(sdtlpdtrp0(xN,X2))
& aSubsetOf0(sdtlpdtrp0(xN,X2),szNzAzT0)
& ! [X3] :
( ~ aElementOf0(X3,sdtlpdtrp0(xN,X2))
| aElementOf0(X3,szNzAzT0) )
& aSet0(sdtlpdtrp0(xN,X2)) ) )
& ( ~ isCountable0(sdtlpdtrp0(xN,X0))
| ( ~ aSubsetOf0(sdtlpdtrp0(xN,X0),szNzAzT0)
& ( ? [X1] :
( aElementOf0(X1,sdtlpdtrp0(xN,X0))
& ~ aElementOf0(X1,szNzAzT0) )
| ~ aSet0(sdtlpdtrp0(xN,X0)) ) ) ) ),
inference(rectify,[],[f202]) ).
fof(f299,plain,
( aElementOf0(sK40,szNzAzT0)
& ! [X2] :
( ~ aElementOf0(X2,szNzAzT0)
| ~ iLess0(X2,sK40)
| ( isCountable0(sdtlpdtrp0(xN,X2))
& aSubsetOf0(sdtlpdtrp0(xN,X2),szNzAzT0)
& ! [X3] :
( ~ aElementOf0(X3,sdtlpdtrp0(xN,X2))
| aElementOf0(X3,szNzAzT0) )
& aSet0(sdtlpdtrp0(xN,X2)) ) )
& ( ~ isCountable0(sdtlpdtrp0(xN,sK40))
| ( ~ aSubsetOf0(sdtlpdtrp0(xN,sK40),szNzAzT0)
& ( ( aElementOf0(sK41,sdtlpdtrp0(xN,sK40))
& ~ aElementOf0(sK41,szNzAzT0) )
| ~ aSet0(sdtlpdtrp0(xN,sK40)) ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK40,sK41]),skolemize(X0,sK40),skolemize(X1,sK41)],[f298]) ).
fof(f300,plain,
! [X0,X1] :
( ~ aSet0(X0)
| ~ aElementOf0(X1,X0)
| aElement0(X1) ),
inference(cnf_transformation,[],[f95]) ).
fof(f307,plain,
! [X3,X0,X1] :
( ~ aSet0(X0)
| ~ aSubsetOf0(X1,X0)
| ~ aElementOf0(X3,X1)
| aElementOf0(X3,X0) ),
inference(cnf_transformation,[],[f224]) ).
fof(f327,plain,
! [X2,X0,X1] :
( ~ sP3(X0,X1)
| sdtmndt0(X1,X0) != X2
| sP2(X2,X1,X0) ),
inference(cnf_transformation,[],[f232]) ).
fof(f338,plain,
! [X0,X1] :
( ~ aElement0(X1)
| ~ aSet0(X0)
| sP3(X1,X0) ),
inference(cnf_transformation,[],[f208]) ).
fof(f347,plain,
aElementOf0(sz00,szNzAzT0),
inference(cnf_transformation,[],[f24]) ).
fof(f349,plain,
! [X0] :
( ~ aElementOf0(X0,szNzAzT0)
| aElementOf0(szszuzczcdt0(X0),szNzAzT0) ),
inference(cnf_transformation,[],[f124]) ).
fof(f351,plain,
! [X0] :
( ~ aElementOf0(X0,szNzAzT0)
| szszuzczcdt0(sK14(X0)) = X0
| sz00 = X0 ),
inference(cnf_transformation,[],[f237]) ).
fof(f352,plain,
! [X0] :
( ~ aElementOf0(X0,szNzAzT0)
| aElementOf0(sK14(X0),szNzAzT0)
| sz00 = X0 ),
inference(cnf_transformation,[],[f237]) ).
fof(f354,plain,
! [X0] :
( ~ aElementOf0(X0,szNzAzT0)
| sdtlseqdt0(sz00,X0) ),
inference(cnf_transformation,[],[f130]) ).
fof(f360,plain,
! [X0,X1] :
( ~ aElementOf0(X1,szNzAzT0)
| ~ aElementOf0(X0,szNzAzT0)
| ~ sdtlseqdt0(X1,X0)
| ~ sdtlseqdt0(X0,X1)
| X0 = X1 ),
inference(cnf_transformation,[],[f137]) ).
fof(f363,plain,
! [X0] :
( ~ aElementOf0(X0,szNzAzT0)
| iLess0(X0,szszuzczcdt0(X0)) ),
inference(cnf_transformation,[],[f142]) ).
fof(f384,plain,
! [X3,X0,X1] :
( ~ aElementOf0(X0,szNzAzT0)
| slbdtrb0(X0) != X1
| ~ aElementOf0(X3,X1)
| aElementOf0(X3,szNzAzT0) ),
inference(cnf_transformation,[],[f253]) ).
fof(f386,plain,
! [X0,X1] :
( ~ aElementOf0(X0,szNzAzT0)
| slbdtrb0(X0) != X1
| aSet0(X1) ),
inference(cnf_transformation,[],[f253]) ).
fof(f446,plain,
isCountable0(xS),
inference(cnf_transformation,[],[f194]) ).
fof(f447,plain,
aSubsetOf0(xS,szNzAzT0),
inference(cnf_transformation,[],[f194]) ).
fof(f500,plain,
! [X0] :
( ~ sP9(X0)
| isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(X0))) ),
inference(cnf_transformation,[],[f293]) ).
fof(f501,plain,
! [X0] :
( ~ sP9(X0)
| aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(X0)),sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0)))) ),
inference(cnf_transformation,[],[f293]) ).
fof(f503,plain,
! [X0] :
( ~ sP9(X0)
| aSet0(sdtlpdtrp0(xN,szszuzczcdt0(X0))) ),
inference(cnf_transformation,[],[f293]) ).
fof(f505,plain,
! [X0] :
( ~ sP9(X0)
| aSet0(sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0)))) ),
inference(cnf_transformation,[],[f293]) ).
fof(f507,plain,
! [X0] :
( ~ sP9(X0)
| aElementOf0(szmzizndt0(sdtlpdtrp0(xN,X0)),sdtlpdtrp0(xN,X0)) ),
inference(cnf_transformation,[],[f293]) ).
fof(f512,plain,
! [X0] :
( ~ aElementOf0(X0,szNzAzT0)
| ~ isCountable0(sdtlpdtrp0(xN,X0))
| ~ aSubsetOf0(sdtlpdtrp0(xN,X0),szNzAzT0)
| sP9(X0) ),
inference(cnf_transformation,[],[f297]) ).
fof(f515,plain,
xS = sdtlpdtrp0(xN,sz00),
inference(cnf_transformation,[],[f297]) ).
fof(f518,plain,
aElementOf0(sK40,szNzAzT0),
inference(cnf_transformation,[],[f299]) ).
fof(f519,plain,
! [X2] :
( ~ aElementOf0(X2,szNzAzT0)
| ~ iLess0(X2,sK40)
| isCountable0(sdtlpdtrp0(xN,X2)) ),
inference(cnf_transformation,[],[f299]) ).
fof(f520,plain,
! [X2] :
( ~ aElementOf0(X2,szNzAzT0)
| ~ iLess0(X2,sK40)
| aSubsetOf0(sdtlpdtrp0(xN,X2),szNzAzT0) ),
inference(cnf_transformation,[],[f299]) ).
fof(f521,plain,
! [X2,X3] :
( ~ aElementOf0(X2,szNzAzT0)
| ~ iLess0(X2,sK40)
| ~ aElementOf0(X3,sdtlpdtrp0(xN,X2))
| aElementOf0(X3,szNzAzT0) ),
inference(cnf_transformation,[],[f299]) ).
fof(f522,plain,
! [X2] :
( ~ aElementOf0(X2,szNzAzT0)
| ~ iLess0(X2,sK40)
| aSet0(sdtlpdtrp0(xN,X2)) ),
inference(cnf_transformation,[],[f299]) ).
fof(f523,plain,
( ~ isCountable0(sdtlpdtrp0(xN,sK40))
| ~ aSubsetOf0(sdtlpdtrp0(xN,sK40),szNzAzT0) ),
inference(cnf_transformation,[],[f299]) ).
fof(f524,plain,
( ~ isCountable0(sdtlpdtrp0(xN,sK40))
| aElementOf0(sK41,sdtlpdtrp0(xN,sK40))
| ~ aSet0(sdtlpdtrp0(xN,sK40)) ),
inference(cnf_transformation,[],[f299]) ).
fof(f525,plain,
( ~ isCountable0(sdtlpdtrp0(xN,sK40))
| ~ aElementOf0(sK41,szNzAzT0)
| ~ aSet0(sdtlpdtrp0(xN,sK40)) ),
inference(cnf_transformation,[],[f299]) ).
fof(f531,plain,
! [X0,X1] :
( ~ sP3(X0,X1)
| sP2(sdtmndt0(X1,X0),X1,X0) ),
inference(equality_resolution,[],[f327]) ).
fof(f538,plain,
! [X0] :
( ~ aElementOf0(X0,szNzAzT0)
| aSet0(slbdtrb0(X0)) ),
inference(equality_resolution,[],[f386]) ).
fof(f540,plain,
! [X3,X0] :
( ~ aElementOf0(X0,szNzAzT0)
| ~ aElementOf0(X3,slbdtrb0(X0))
| aElementOf0(X3,szNzAzT0) ),
inference(equality_resolution,[],[f384]) ).
tcf(c_49,plain,
! [X0: $i,X1: $i] :
( aElement0(X0)
| ~ aSet0(X1)
| ~ aElementOf0(X0,X1) ),
inference(cnf_transformation,[],[f300]) ).
tcf(c_59,plain,
! [X0: $i,X1: $i,X2: $i] :
( aElementOf0(X0,X2)
| ~ aSet0(X2)
| ~ aSubsetOf0(X1,X2)
| ~ aElementOf0(X0,X1) ),
inference(cnf_transformation,[],[f307]) ).
tcf(c_77,plain,
! [X0: $i,X1: $i] :
( sP2(sdtmndt0(X1,X0),X1,X0)
| ~ sP3(X0,X1) ),
inference(cnf_transformation,[],[f531]) ).
tcf(c_87,plain,
! [X0: $i,X1: $i] :
( sP3(X0,X1)
| ~ aSet0(X1)
| ~ aElement0(X0) ),
inference(cnf_transformation,[],[f338]) ).
tcf(c_96,plain,
aElementOf0(sz00,szNzAzT0),
inference(cnf_transformation,[],[f347]) ).
tcf(c_97,plain,
! [X0: $i] :
( aElementOf0(szszuzczcdt0(X0),szNzAzT0)
| ~ aElementOf0(X0,szNzAzT0) ),
inference(cnf_transformation,[],[f349]) ).
tcf(c_100,plain,
! [X0: $i] :
( aElementOf0(sK14(X0),szNzAzT0)
| ( X0 = sz00 )
| ~ aElementOf0(X0,szNzAzT0) ),
inference(cnf_transformation,[],[f352]) ).
tcf(c_101,plain,
! [X0: $i] :
( ( X0 = sz00 )
| ( szszuzczcdt0(sK14(X0)) = X0 )
| ~ aElementOf0(X0,szNzAzT0) ),
inference(cnf_transformation,[],[f351]) ).
tcf(c_103,plain,
! [X0: $i] :
( sdtlseqdt0(sz00,X0)
| ~ aElementOf0(X0,szNzAzT0) ),
inference(cnf_transformation,[],[f354]) ).
tcf(c_109,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ~ aElementOf0(X1,szNzAzT0)
| ~ aElementOf0(X0,szNzAzT0)
| ~ sdtlseqdt0(X1,X0)
| ~ sdtlseqdt0(X0,X1) ),
inference(cnf_transformation,[],[f360]) ).
tcf(c_112,plain,
! [X0: $i] :
( iLess0(X0,szszuzczcdt0(X0))
| ~ aElementOf0(X0,szNzAzT0) ),
inference(cnf_transformation,[],[f363]) ).
tcf(c_135,plain,
! [X0: $i] :
( aSet0(slbdtrb0(X0))
| ~ aElementOf0(X0,szNzAzT0) ),
inference(cnf_transformation,[],[f538]) ).
tcf(c_137,plain,
! [X0: $i,X1: $i] :
( aElementOf0(X0,szNzAzT0)
| ~ aElementOf0(X1,szNzAzT0)
| ~ aElementOf0(X0,slbdtrb0(X1)) ),
inference(cnf_transformation,[],[f540]) ).
tcf(c_142,plain,
! [X0: $i] :
( aElementOf0(X0,slbdtrb0(szszuzczcdt0(X0)))
| ~ aElementOf0(X0,szNzAzT0) ),
inference(cnf_transformation,[],[f569]) ).
tcf(c_197,plain,
aSubsetOf0(xS,szNzAzT0),
inference(cnf_transformation,[],[f447]) ).
tcf(c_198,plain,
isCountable0(xS),
inference(cnf_transformation,[],[f446]) ).
tcf(c_249,plain,
! [X0: $i] :
( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,X0)),sdtlpdtrp0(xN,X0))
| ~ sP9(X0) ),
inference(cnf_transformation,[],[f507]) ).
tcf(c_251,plain,
! [X0: $i] :
( aSet0(sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
| ~ sP9(X0) ),
inference(cnf_transformation,[],[f505]) ).
tcf(c_253,plain,
! [X0: $i] :
( aSet0(sdtlpdtrp0(xN,szszuzczcdt0(X0)))
| ~ sP9(X0) ),
inference(cnf_transformation,[],[f503]) ).
tcf(c_255,plain,
! [X0: $i] :
( aSubsetOf0(sdtlpdtrp0(xN,szszuzczcdt0(X0)),sdtmndt0(sdtlpdtrp0(xN,X0),szmzizndt0(sdtlpdtrp0(xN,X0))))
| ~ sP9(X0) ),
inference(cnf_transformation,[],[f501]) ).
tcf(c_256,plain,
! [X0: $i] :
( isCountable0(sdtlpdtrp0(xN,szszuzczcdt0(X0)))
| ~ sP9(X0) ),
inference(cnf_transformation,[],[f500]) ).
tcf(c_263,plain,
sdtlpdtrp0(xN,sz00) = xS,
inference(cnf_transformation,[],[f515]) ).
tcf(c_266,plain,
! [X0: $i] :
( sP9(X0)
| ~ aElementOf0(X0,szNzAzT0)
| ~ isCountable0(sdtlpdtrp0(xN,X0))
| ~ aSubsetOf0(sdtlpdtrp0(xN,X0),szNzAzT0) ),
inference(cnf_transformation,[],[f512]) ).
tcf(c_267,negated_conjecture,
( ~ aElementOf0(sK41,szNzAzT0)
| ~ isCountable0(sdtlpdtrp0(xN,sK40))
| ~ aSet0(sdtlpdtrp0(xN,sK40)) ),
inference(cnf_transformation,[],[f525]) ).
tcf(c_268,negated_conjecture,
( aElementOf0(sK41,sdtlpdtrp0(xN,sK40))
| ~ isCountable0(sdtlpdtrp0(xN,sK40))
| ~ aSet0(sdtlpdtrp0(xN,sK40)) ),
inference(cnf_transformation,[],[f524]) ).
tcf(c_269,negated_conjecture,
( ~ isCountable0(sdtlpdtrp0(xN,sK40))
| ~ aSubsetOf0(sdtlpdtrp0(xN,sK40),szNzAzT0) ),
inference(cnf_transformation,[],[f523]) ).
tcf(c_270,negated_conjecture,
! [X0: $i] :
( aSet0(sdtlpdtrp0(xN,X0))
| ~ iLess0(X0,sK40)
| ~ aElementOf0(X0,szNzAzT0) ),
inference(cnf_transformation,[],[f522]) ).
tcf(c_271,negated_conjecture,
! [X0: $i,X1: $i] :
( aElementOf0(X0,szNzAzT0)
| ~ iLess0(X1,sK40)
| ~ aElementOf0(X1,szNzAzT0)
| ~ aElementOf0(X0,sdtlpdtrp0(xN,X1)) ),
inference(cnf_transformation,[],[f521]) ).
tcf(c_272,negated_conjecture,
! [X0: $i] :
( aSubsetOf0(sdtlpdtrp0(xN,X0),szNzAzT0)
| ~ iLess0(X0,sK40)
| ~ aElementOf0(X0,szNzAzT0) ),
inference(cnf_transformation,[],[f520]) ).
tcf(c_273,negated_conjecture,
! [X0: $i] :
( isCountable0(sdtlpdtrp0(xN,X0))
| ~ iLess0(X0,sK40)
| ~ aElementOf0(X0,szNzAzT0) ),
inference(cnf_transformation,[],[f519]) ).
tcf(c_274,negated_conjecture,
aElementOf0(sK40,szNzAzT0),
inference(cnf_transformation,[],[f518]) ).
tcf(c_474,plain,
! [X0: $i,X1: $i] :
( sP2(sdtmndt0(X1,X0),X1,X0)
| ~ sP3(X0,X1) ),
inference(prop_impl_just,[status(thm)],[c_77]) ).
tcf(c_490,plain,
! [X0: $i] :
( iLess0(X0,szszuzczcdt0(X0))
| ~ aElementOf0(X0,szNzAzT0) ),
inference(prop_impl_just,[status(thm)],[c_112]) ).
tcf(c_2259,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( sP2(sdtmndt0(X3,X1),X3,X1)
| ~ aSet0(X2)
| ~ aElement0(X0)
| ( X2 != X3 )
| ( X0 != X1 ) ),
inference(resolution_lifted,[status(thm)],[c_87,c_474]) ).
tcf(c_2260,plain,
! [X0: $i,X1: $i] :
( sP2(sdtmndt0(X1,X0),X1,X0)
| ~ aSet0(X1)
| ~ aElement0(X0) ),
inference(unflattening,[status(thm)],[c_2259]) ).
tcf(c_2531,plain,
! [X0: $i,X1: $i] :
( isCountable0(sdtlpdtrp0(xN,X1))
| ~ aElementOf0(X1,szNzAzT0)
| ~ aElementOf0(X0,szNzAzT0)
| ( X0 != X1 )
| ( szszuzczcdt0(X0) != sK40 ) ),
inference(resolution_lifted,[status(thm)],[c_490,c_273]) ).
tcf(c_2532,plain,
! [X0: $i] :
( isCountable0(sdtlpdtrp0(xN,X0))
| ~ aElementOf0(X0,szNzAzT0)
| ( szszuzczcdt0(X0) != sK40 ) ),
inference(unflattening,[status(thm)],[c_2531]) ).
tcf(c_2543,plain,
! [X0: $i,X1: $i] :
( aSubsetOf0(sdtlpdtrp0(xN,X1),szNzAzT0)
| ~ aElementOf0(X1,szNzAzT0)
| ~ aElementOf0(X0,szNzAzT0)
| ( X0 != X1 )
| ( szszuzczcdt0(X0) != sK40 ) ),
inference(resolution_lifted,[status(thm)],[c_490,c_272]) ).
tcf(c_2544,plain,
! [X0: $i] :
( aSubsetOf0(sdtlpdtrp0(xN,X0),szNzAzT0)
| ~ aElementOf0(X0,szNzAzT0)
| ( szszuzczcdt0(X0) != sK40 ) ),
inference(unflattening,[status(thm)],[c_2543]) ).
tcf(c_2555,plain,
! [X0: $i,X1: $i] :
( aSet0(sdtlpdtrp0(xN,X1))
| ~ aElementOf0(X1,szNzAzT0)
| ~ aElementOf0(X0,szNzAzT0)
| ( X0 != X1 )
| ( szszuzczcdt0(X0) != sK40 ) ),
inference(resolution_lifted,[status(thm)],[c_490,c_270]) ).
tcf(c_2556,plain,
! [X0: $i] :
( aSet0(sdtlpdtrp0(xN,X0))
| ~ aElementOf0(X0,szNzAzT0)
| ( szszuzczcdt0(X0) != sK40 ) ),
inference(unflattening,[status(thm)],[c_2555]) ).
tcf(c_2567,plain,
! [X0: $i,X1: $i,X2: $i] :
( aElementOf0(X2,szNzAzT0)
| ~ aElementOf0(X1,szNzAzT0)
| ~ aElementOf0(X0,szNzAzT0)
| ~ aElementOf0(X2,sdtlpdtrp0(xN,X1))
| ( X0 != X1 )
| ( szszuzczcdt0(X0) != sK40 ) ),
inference(resolution_lifted,[status(thm)],[c_490,c_271]) ).
tcf(c_2568,plain,
! [X0: $i,X1: $i] :
( aElementOf0(X1,szNzAzT0)
| ~ aElementOf0(X0,szNzAzT0)
| ~ aElementOf0(X1,sdtlpdtrp0(xN,X0))
| ( szszuzczcdt0(X0) != sK40 ) ),
inference(unflattening,[status(thm)],[c_2567]) ).
tcf(c_24291,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X2 = X0 )
| ( X2 != X1 )
| ( X0 != X1 ) ),
theory(equality) ).
tcf(c_24296,plain,
! [X0: $i,X1: $i] :
( isCountable0(X0)
| ~ isCountable0(X1)
| ( X0 != X1 ) ),
theory(equality) ).
tcf(c_28126,plain,
( sdtlseqdt0(sz00,sz00)
| ~ aElementOf0(sz00,szNzAzT0) ),
inference(instantiation,[status(thm)],[c_103]) ).
tcf(c_28144,plain,
( aElementOf0(sK14(sK40),szNzAzT0)
| ( sK40 = sz00 )
| ~ aElementOf0(sK40,szNzAzT0) ),
inference(instantiation,[status(thm)],[c_100]) ).
tcf(c_28206,plain,
! [X0: $i,X1: $i] :
( isCountable0(sdtlpdtrp0(xN,X0))
| ~ isCountable0(X1)
| ( sdtlpdtrp0(xN,X0) != X1 ) ),
inference(instantiation,[status(thm)],[c_24296]) ).
tcf(c_28281,plain,
! [X0: $i] :
( aSet0(slbdtrb0(szszuzczcdt0(X0)))
| ~ aElementOf0(X0,szNzAzT0) ),
inference(superposition,[status(thm)],[c_97,c_135]) ).
tcf(c_28393,plain,
! [X0: $i] :
( aElement0(X0)
| ~ aElementOf0(X0,szNzAzT0)
| ~ aSet0(slbdtrb0(szszuzczcdt0(X0))) ),
inference(superposition,[status(thm)],[c_142,c_49]) ).
tcf(c_28826,plain,
! [X0: $i] :
( aElement0(X0)
| ~ aElementOf0(X0,szNzAzT0) ),
inference(global_subsumption_just,[status(thm)],[c_28393,c_28281,c_28393]) ).
tcf(c_29367,plain,
! [X0: $i,X1: $i] :
( ( X0 = sK40 )
| ( sK40 != X1 )
| ( X0 != X1 ) ),
inference(instantiation,[status(thm)],[c_24291]) ).
tcf(c_29603,plain,
( ( sz00 = sz00 )
| ~ sdtlseqdt0(sz00,sz00)
| ~ aElementOf0(sz00,szNzAzT0) ),
inference(instantiation,[status(thm)],[c_109]) ).
tcf(c_30715,plain,
( ( sz00 = sK40 )
| ( szszuzczcdt0(sK14(sK40)) = sK40 ) ),
inference(superposition,[status(thm)],[c_274,c_101]) ).
tcf(c_30826,plain,
( aElementOf0(sK14(sK40),slbdtrb0(sK40))
| ( sz00 = sK40 )
| ~ aElementOf0(sK14(sK40),szNzAzT0) ),
inference(superposition,[status(thm)],[c_30715,c_142]) ).
tcf(c_30831,plain,
( isCountable0(sdtlpdtrp0(xN,sK40))
| ( sz00 = sK40 )
| ~ sP9(sK14(sK40)) ),
inference(superposition,[status(thm)],[c_30715,c_256]) ).
tcf(c_30832,plain,
( aSet0(sdtlpdtrp0(xN,sK40))
| ( sz00 = sK40 )
| ~ sP9(sK14(sK40)) ),
inference(superposition,[status(thm)],[c_30715,c_253]) ).
tcf(c_30835,plain,
! [X0: $i] :
( aElementOf0(X0,szNzAzT0)
| ( sz00 = sK40 )
| ~ aElementOf0(sK14(sK40),szNzAzT0)
| ~ aElementOf0(X0,sdtlpdtrp0(xN,sK14(sK40))) ),
inference(superposition,[status(thm)],[c_30715,c_2568]) ).
tcf(c_30837,plain,
( aSet0(sdtlpdtrp0(xN,sK14(sK40)))
| ( sz00 = sK40 )
| ~ aElementOf0(sK14(sK40),szNzAzT0) ),
inference(superposition,[status(thm)],[c_30715,c_2556]) ).
tcf(c_30838,plain,
( isCountable0(sdtlpdtrp0(xN,sK14(sK40)))
| ( sz00 = sK40 )
| ~ aElementOf0(sK14(sK40),szNzAzT0) ),
inference(superposition,[status(thm)],[c_30715,c_2532]) ).
tcf(c_30921,plain,
( ( sz00 = sK40 )
| ~ sP9(sK14(sK40))
| ~ aElementOf0(sK41,szNzAzT0)
| ~ isCountable0(sdtlpdtrp0(xN,sK40)) ),
inference(superposition,[status(thm)],[c_30832,c_267]) ).
tcf(c_31672,plain,
( isCountable0(sdtlpdtrp0(xN,sz00))
| ~ isCountable0(xS)
| ( sdtlpdtrp0(xN,sz00) != xS ) ),
inference(instantiation,[status(thm)],[c_28206]) ).
tcf(c_32394,plain,
( aSubsetOf0(sdtlpdtrp0(xN,sK40),sdtmndt0(sdtlpdtrp0(xN,sK14(sK40)),szmzizndt0(sdtlpdtrp0(xN,sK14(sK40)))))
| ( sz00 = sK40 )
| ~ sP9(sK14(sK40)) ),
inference(superposition,[status(thm)],[c_30715,c_255]) ).
tcf(c_34377,plain,
! [X0: $i] :
( aElementOf0(sK41,X0)
| ~ aSet0(X0)
| ~ isCountable0(sdtlpdtrp0(xN,sK40))
| ~ aSet0(sdtlpdtrp0(xN,sK40))
| ~ aSubsetOf0(sdtlpdtrp0(xN,sK40),X0) ),
inference(superposition,[status(thm)],[c_268,c_59]) ).
tcf(c_34410,plain,
( ( sz00 = sK40 )
| ( szszuzczcdt0(sK14(sK40)) = sK40 ) ),
inference(superposition,[status(thm)],[c_274,c_101]) ).
tcf(c_34517,plain,
( aSubsetOf0(sdtlpdtrp0(xN,sK14(sK40)),szNzAzT0)
| ( sz00 = sK40 )
| ~ aElementOf0(sK14(sK40),szNzAzT0) ),
inference(superposition,[status(thm)],[c_34410,c_2544]) ).
tcf(c_34550,plain,
! [X0: $i] :
( ( X0 = sK40 )
| ( sK40 != sz00 )
| ( X0 != sz00 ) ),
inference(instantiation,[status(thm)],[c_29367]) ).
tcf(c_35577,plain,
( aSubsetOf0(sdtlpdtrp0(xN,sK40),sdtmndt0(sdtlpdtrp0(xN,sK14(sK40)),szmzizndt0(sdtlpdtrp0(xN,sK14(sK40)))))
| ( sz00 = sK40 )
| ~ sP9(sK14(sK40)) ),
inference(superposition,[status(thm)],[c_34410,c_255]) ).
tcf(c_35836,plain,
( aElementOf0(sK41,sdtmndt0(sdtlpdtrp0(xN,sK14(sK40)),szmzizndt0(sdtlpdtrp0(xN,sK14(sK40)))))
| ( sz00 = sK40 )
| ~ sP9(sK14(sK40))
| ~ isCountable0(sdtlpdtrp0(xN,sK40))
| ~ aSet0(sdtlpdtrp0(xN,sK40))
| ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,sK14(sK40)),szmzizndt0(sdtlpdtrp0(xN,sK14(sK40))))) ),
inference(superposition,[status(thm)],[c_35577,c_34377]) ).
tcf(c_35885,plain,
( aElementOf0(sK41,sdtmndt0(sdtlpdtrp0(xN,sK14(sK40)),szmzizndt0(sdtlpdtrp0(xN,sK14(sK40)))))
| ( sz00 = sK40 )
| ~ sP9(sK14(sK40))
| ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,sK14(sK40)),szmzizndt0(sdtlpdtrp0(xN,sK14(sK40))))) ),
inference(global_subsumption_just,[status(thm)],[c_35836,c_30832,c_30831,c_35836]) ).
tcf(c_36301,plain,
( sP9(sK14(sK40))
| ( sz00 = sK40 )
| ~ aElementOf0(sK14(sK40),szNzAzT0)
| ~ isCountable0(sdtlpdtrp0(xN,sK14(sK40))) ),
inference(superposition,[status(thm)],[c_34517,c_266]) ).
tcf(c_36692,plain,
( sP9(sK14(sK40))
| ( sz00 = sK40 )
| ~ aElementOf0(sK14(sK40),szNzAzT0) ),
inference(global_subsumption_just,[status(thm)],[c_36301,c_30838,c_36301]) ).
tcf(c_36695,plain,
( sP9(sK14(sK40))
| ( sz00 = sK40 )
| ~ aElementOf0(sK40,szNzAzT0) ),
inference(superposition,[status(thm)],[c_100,c_36692]) ).
tcf(c_37475,plain,
( ( sz00 = sK40 )
| ( sK40 != sz00 )
| ( sz00 != sz00 ) ),
inference(instantiation,[status(thm)],[c_34550]) ).
tcf(c_41604,plain,
! [X0: $i] :
( aElement0(X0)
| ~ aElementOf0(X0,szNzAzT0)
| ~ aSet0(slbdtrb0(szszuzczcdt0(X0))) ),
inference(superposition,[status(thm)],[c_142,c_49]) ).
tcf(c_41758,plain,
! [X0: $i] :
( aElement0(X0)
| ~ aElementOf0(X0,szNzAzT0) ),
inference(global_subsumption_just,[status(thm)],[c_41604,c_28826]) ).
tcf(c_42645,plain,
! [X0: $i] :
( aElementOf0(sK41,X0)
| ~ aSet0(X0)
| ~ isCountable0(sdtlpdtrp0(xN,sK40))
| ~ aSet0(sdtlpdtrp0(xN,sK40))
| ~ aSubsetOf0(sdtlpdtrp0(xN,sK40),X0) ),
inference(superposition,[status(thm)],[c_268,c_59]) ).
tcf(c_42664,plain,
( ( sz00 = sK40 )
| ( szszuzczcdt0(sK14(sK40)) = sK40 ) ),
inference(superposition,[status(thm)],[c_274,c_101]) ).
tcf(c_42805,plain,
( aElementOf0(sK14(sK40),slbdtrb0(sK40))
| ( sz00 = sK40 )
| ~ aElementOf0(sK14(sK40),szNzAzT0) ),
inference(superposition,[status(thm)],[c_42664,c_142]) ).
tcf(c_42810,plain,
( isCountable0(sdtlpdtrp0(xN,sK40))
| ( sz00 = sK40 )
| ~ sP9(sK14(sK40)) ),
inference(superposition,[status(thm)],[c_42664,c_256]) ).
tcf(c_42811,plain,
( aSet0(sdtlpdtrp0(xN,sK40))
| ( sz00 = sK40 )
| ~ sP9(sK14(sK40)) ),
inference(superposition,[status(thm)],[c_42664,c_253]) ).
tcf(c_42814,plain,
! [X0: $i] :
( aElementOf0(X0,szNzAzT0)
| ( sz00 = sK40 )
| ~ aElementOf0(sK14(sK40),szNzAzT0)
| ~ aElementOf0(X0,sdtlpdtrp0(xN,sK14(sK40))) ),
inference(superposition,[status(thm)],[c_42664,c_2568]) ).
tcf(c_42816,plain,
( aSet0(sdtlpdtrp0(xN,sK14(sK40)))
| ( sz00 = sK40 )
| ~ aElementOf0(sK14(sK40),szNzAzT0) ),
inference(superposition,[status(thm)],[c_42664,c_2556]) ).
tcf(c_42839,plain,
( isCountable0(sdtlpdtrp0(xN,sK40))
| ( sz00 = sK40 ) ),
inference(global_subsumption_just,[status(thm)],[c_42810,c_274,c_30831,c_36695]) ).
tcf(c_42841,plain,
( aSet0(sdtlpdtrp0(xN,sK40))
| ( sz00 = sK40 ) ),
inference(global_subsumption_just,[status(thm)],[c_42811,c_274,c_30832,c_36695]) ).
tcf(c_42845,plain,
( ( sz00 = sK40 )
| ~ aElementOf0(sK41,szNzAzT0)
| ~ isCountable0(sdtlpdtrp0(xN,sK40)) ),
inference(superposition,[status(thm)],[c_42841,c_267]) ).
tcf(c_42860,plain,
( ( sz00 = sK40 )
| ~ aElementOf0(sK41,szNzAzT0) ),
inference(global_subsumption_just,[status(thm)],[c_42845,c_274,c_30921,c_36695,c_42839]) ).
tcf(c_42998,plain,
( aElementOf0(sK14(sK40),slbdtrb0(sK40))
| ( sz00 = sK40 ) ),
inference(global_subsumption_just,[status(thm)],[c_42805,c_274,c_96,c_28126,c_28144,c_29603,c_30826,c_37475]) ).
tcf(c_43003,plain,
( aElementOf0(sK14(sK40),szNzAzT0)
| ( sz00 = sK40 )
| ~ aElementOf0(sK40,szNzAzT0) ),
inference(superposition,[status(thm)],[c_42998,c_137]) ).
tcf(c_43005,plain,
( aSet0(sdtlpdtrp0(xN,sK14(sK40)))
| ( sz00 = sK40 ) ),
inference(global_subsumption_just,[status(thm)],[c_42816,c_274,c_30837,c_43003]) ).
tcf(c_43408,plain,
! [X0: $i] :
( aElementOf0(X0,szNzAzT0)
| ( sz00 = sK40 )
| ~ aElementOf0(X0,sdtlpdtrp0(xN,sK14(sK40))) ),
inference(global_subsumption_just,[status(thm)],[c_42814,c_274,c_30835,c_43003]) ).
tcf(c_43415,plain,
( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,sK14(sK40))),szNzAzT0)
| ( sz00 = sK40 )
| ~ sP9(sK14(sK40)) ),
inference(superposition,[status(thm)],[c_249,c_43408]) ).
tcf(c_43728,plain,
( aElementOf0(sK14(sK40),szNzAzT0)
| ( sz00 = sK40 ) ),
inference(global_subsumption_just,[status(thm)],[c_43003,c_274,c_43003]) ).
tcf(c_43870,plain,
( aElementOf0(szmzizndt0(sdtlpdtrp0(xN,sK14(sK40))),szNzAzT0)
| ( sz00 = sK40 ) ),
inference(global_subsumption_just,[status(thm)],[c_43415,c_274,c_36695,c_43415]) ).
tcf(c_43878,plain,
( aElement0(szmzizndt0(sdtlpdtrp0(xN,sK14(sK40))))
| ( sz00 = sK40 ) ),
inference(superposition,[status(thm)],[c_43870,c_41758]) ).
tcf(c_43903,plain,
( aSubsetOf0(sdtlpdtrp0(xN,sK40),sdtmndt0(sdtlpdtrp0(xN,sK14(sK40)),szmzizndt0(sdtlpdtrp0(xN,sK14(sK40)))))
| ( sz00 = sK40 )
| ~ sP9(sK14(sK40)) ),
inference(superposition,[status(thm)],[c_42664,c_255]) ).
tcf(c_44114,plain,
( aSubsetOf0(sdtlpdtrp0(xN,sK40),sdtmndt0(sdtlpdtrp0(xN,sK14(sK40)),szmzizndt0(sdtlpdtrp0(xN,sK14(sK40)))))
| ( sz00 = sK40 ) ),
inference(global_subsumption_just,[status(thm)],[c_43903,c_274,c_32394,c_36695]) ).
tcf(c_44118,plain,
( aElementOf0(sK41,sdtmndt0(sdtlpdtrp0(xN,sK14(sK40)),szmzizndt0(sdtlpdtrp0(xN,sK14(sK40)))))
| ( sz00 = sK40 )
| ~ isCountable0(sdtlpdtrp0(xN,sK40))
| ~ aSet0(sdtlpdtrp0(xN,sK40))
| ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,sK14(sK40)),szmzizndt0(sdtlpdtrp0(xN,sK14(sK40))))) ),
inference(superposition,[status(thm)],[c_44114,c_42645]) ).
tcf(c_44134,plain,
( aElementOf0(sK41,sdtmndt0(sdtlpdtrp0(xN,sK14(sK40)),szmzizndt0(sdtlpdtrp0(xN,sK14(sK40)))))
| ( sz00 = sK40 )
| ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,sK14(sK40)),szmzizndt0(sdtlpdtrp0(xN,sK14(sK40))))) ),
inference(global_subsumption_just,[status(thm)],[c_44118,c_274,c_35885,c_36695]) ).
tcf(c_60046,plain,
! [X0: $i] :
( aElementOf0(sK41,X0)
| ~ aSet0(X0)
| ~ isCountable0(sdtlpdtrp0(xN,sK40))
| ~ aSet0(sdtlpdtrp0(xN,sK40))
| ~ aSubsetOf0(sdtlpdtrp0(xN,sK40),X0) ),
inference(superposition,[status(thm)],[c_268,c_59]) ).
tcf(c_60283,plain,
( ( sz00 = sK40 )
| ( szszuzczcdt0(sK14(sK40)) = sK40 ) ),
inference(superposition,[status(thm)],[c_274,c_101]) ).
tcf(c_61216,plain,
( aSubsetOf0(sdtlpdtrp0(xN,sK40),sdtmndt0(sdtlpdtrp0(xN,sK14(sK40)),szmzizndt0(sdtlpdtrp0(xN,sK14(sK40)))))
| ( sz00 = sK40 )
| ~ sP9(sK14(sK40)) ),
inference(superposition,[status(thm)],[c_60283,c_255]) ).
tcf(c_61256,plain,
( aSubsetOf0(sdtlpdtrp0(xN,sK40),sdtmndt0(sdtlpdtrp0(xN,sK14(sK40)),szmzizndt0(sdtlpdtrp0(xN,sK14(sK40)))))
| ( sz00 = sK40 ) ),
inference(global_subsumption_just,[status(thm)],[c_61216,c_44114]) ).
tcf(c_61260,plain,
( aElementOf0(sK41,sdtmndt0(sdtlpdtrp0(xN,sK14(sK40)),szmzizndt0(sdtlpdtrp0(xN,sK14(sK40)))))
| ( sz00 = sK40 )
| ~ isCountable0(sdtlpdtrp0(xN,sK40))
| ~ aSet0(sdtlpdtrp0(xN,sK40))
| ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,sK14(sK40)),szmzizndt0(sdtlpdtrp0(xN,sK14(sK40))))) ),
inference(superposition,[status(thm)],[c_61256,c_60046]) ).
tcf(c_61267,plain,
( aElementOf0(sK41,sdtmndt0(sdtlpdtrp0(xN,sK14(sK40)),szmzizndt0(sdtlpdtrp0(xN,sK14(sK40)))))
| ( sz00 = sK40 )
| ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,sK14(sK40)),szmzizndt0(sdtlpdtrp0(xN,sK14(sK40))))) ),
inference(global_subsumption_just,[status(thm)],[c_61260,c_44134]) ).
tcf(c_70140,plain,
! [X0: $i] :
( aElementOf0(X0,szNzAzT0)
| ~ aElementOf0(sK14(sK40),szNzAzT0)
| ~ aElementOf0(X0,sdtlpdtrp0(xN,sK14(sK40)))
| ( szszuzczcdt0(sK14(sK40)) != sK40 ) ),
inference(instantiation,[status(thm)],[c_2568]) ).
tcf(c_71032,plain,
( aElementOf0(sK41,szNzAzT0)
| ~ aElementOf0(sK14(sK40),szNzAzT0)
| ~ aElementOf0(sK41,sdtlpdtrp0(xN,sK14(sK40)))
| ( szszuzczcdt0(sK14(sK40)) != sK40 ) ),
inference(instantiation,[status(thm)],[c_70140]) ).
tcf(c_90398,plain,
! [X0: $i] :
( aElementOf0(sK41,X0)
| ~ aSet0(X0)
| ~ isCountable0(sdtlpdtrp0(xN,sK40))
| ~ aSet0(sdtlpdtrp0(xN,sK40))
| ~ aSubsetOf0(sdtlpdtrp0(xN,sK40),X0) ),
inference(superposition,[status(thm)],[c_268,c_59]) ).
tcf(c_90491,plain,
( ( sz00 = sK40 )
| ( szszuzczcdt0(sK14(sK40)) = sK40 ) ),
inference(superposition,[status(thm)],[c_274,c_101]) ).
tcf(c_91483,plain,
( aSubsetOf0(sdtlpdtrp0(xN,sK40),sdtmndt0(sdtlpdtrp0(xN,sK14(sK40)),szmzizndt0(sdtlpdtrp0(xN,sK14(sK40)))))
| ( sz00 = sK40 )
| ~ sP9(sK14(sK40)) ),
inference(superposition,[status(thm)],[c_90491,c_255]) ).
tcf(c_91766,plain,
( aSubsetOf0(sdtlpdtrp0(xN,sK40),sdtmndt0(sdtlpdtrp0(xN,sK14(sK40)),szmzizndt0(sdtlpdtrp0(xN,sK14(sK40)))))
| ( sz00 = sK40 ) ),
inference(global_subsumption_just,[status(thm)],[c_91483,c_44114]) ).
tcf(c_91770,plain,
( aElementOf0(sK41,sdtmndt0(sdtlpdtrp0(xN,sK14(sK40)),szmzizndt0(sdtlpdtrp0(xN,sK14(sK40)))))
| ( sz00 = sK40 )
| ~ isCountable0(sdtlpdtrp0(xN,sK40))
| ~ aSet0(sdtlpdtrp0(xN,sK40))
| ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,sK14(sK40)),szmzizndt0(sdtlpdtrp0(xN,sK14(sK40))))) ),
inference(superposition,[status(thm)],[c_91766,c_90398]) ).
fof(f206,definition,
! [X2,X0,X1] :
( sP2(X2,X0,X1)
<=> ( ! [X3] :
( aElementOf0(X3,X2)
<=> ( X3 != X1
& aElementOf0(X3,X0)
& aElement0(X3) ) )
& aSet0(X2) ) ),
introduced(definition,[new_symbols(definition,[sP2])],[predicate_definition_introduction]) ).
fof(f207,definition,
! [X1,X0] :
( ~ sP3(X1,X0)
| ! [X2] :
( X2 = sdtmndt0(X0,X1)
<=> sP2(X2,X0,X1) ) ),
introduced(definition,[new_symbols(definition,[sP3])],[predicate_definition_introduction]) ).
fof(f208,plain,
! [X0,X1] :
( ~ aElement0(X1)
| ~ aSet0(X0)
| sP3(X1,X0) ),
inference(definition_folding,[],[f112,f207,f206]) ).
fof(f233,plain,
! [X2,X0,X1] :
( ( ~ sP2(X2,X0,X1)
| ( ! [X3] :
( ( ~ aElementOf0(X3,X2)
| ( X3 != X1
& aElementOf0(X3,X0)
& aElement0(X3) ) )
& ( X1 = X3
| ~ aElementOf0(X3,X0)
| ~ aElement0(X3)
| aElementOf0(X3,X2) ) )
& aSet0(X2) ) )
& ( ? [X3] :
( ( aElementOf0(X3,X2)
| ( X3 != X1
& aElementOf0(X3,X0)
& aElement0(X3) ) )
& ( ~ aElementOf0(X3,X2)
| X1 = X3
| ~ aElementOf0(X3,X0)
| ~ aElement0(X3) ) )
| ~ aSet0(X2)
| sP2(X2,X0,X1) ) ),
inference(nnf_transformation,[],[f206]) ).
fof(f234,plain,
! [X2,X0,X1] :
( ( ~ sP2(X2,X0,X1)
| ( ! [X3] :
( ( ~ aElementOf0(X3,X2)
| ( X3 != X1
& aElementOf0(X3,X0)
& aElement0(X3) ) )
& ( X1 = X3
| ~ aElementOf0(X3,X0)
| ~ aElement0(X3)
| aElementOf0(X3,X2) ) )
& aSet0(X2) ) )
& ( ? [X3] :
( ( aElementOf0(X3,X2)
| ( X3 != X1
& aElementOf0(X3,X0)
& aElement0(X3) ) )
& ( ~ aElementOf0(X3,X2)
| X1 = X3
| ~ aElementOf0(X3,X0)
| ~ aElement0(X3) ) )
| ~ aSet0(X2)
| sP2(X2,X0,X1) ) ),
inference(flattening,[],[f233]) ).
fof(f235,plain,
! [X0,X1,X2] :
( ( ~ sP2(X0,X1,X2)
| ( ! [X4] :
( ( ~ aElementOf0(X4,X0)
| ( X2 != X4
& aElementOf0(X4,X1)
& aElement0(X4) ) )
& ( X2 = X4
| ~ aElementOf0(X4,X1)
| ~ aElement0(X4)
| aElementOf0(X4,X0) ) )
& aSet0(X0) ) )
& ( ? [X3] :
( ( aElementOf0(X3,X0)
| ( X2 != X3
& aElementOf0(X3,X1)
& aElement0(X3) ) )
& ( ~ aElementOf0(X3,X0)
| X2 = X3
| ~ aElementOf0(X3,X1)
| ~ aElement0(X3) ) )
| ~ aSet0(X0)
| sP2(X0,X1,X2) ) ),
inference(rectify,[],[f234]) ).
fof(f236,plain,
! [X0,X1,X2] :
( ( ~ sP2(X0,X1,X2)
| ( ! [X4] :
( ( ~ aElementOf0(X4,X0)
| ( X2 != X4
& aElementOf0(X4,X1)
& aElement0(X4) ) )
& ( X2 = X4
| ~ aElementOf0(X4,X1)
| ~ aElement0(X4)
| aElementOf0(X4,X0) ) )
& aSet0(X0) ) )
& ( ( ( aElementOf0(sK13(X0,X1,X2),X0)
| ( sK13(X0,X1,X2) != X2
& aElementOf0(sK13(X0,X1,X2),X1)
& aElement0(sK13(X0,X1,X2)) ) )
& ( ~ aElementOf0(sK13(X0,X1,X2),X0)
| sK13(X0,X1,X2) = X2
| ~ aElementOf0(sK13(X0,X1,X2),X1)
| ~ aElement0(sK13(X0,X1,X2)) ) )
| ~ aSet0(X0)
| sP2(X0,X1,X2) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK13]),skolemize(X3,sK13(X0,X1,X2))],[f235]) ).
fof(f330,plain,
! [X2,X0,X1,X4] :
( ~ sP2(X0,X1,X2)
| ~ aElementOf0(X4,X0)
| aElementOf0(X4,X1) ),
inference(cnf_transformation,[],[f236]) ).
tcf(c_85,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( aElementOf0(X3,X1)
| ~ aElementOf0(X3,X0)
| ~ sP2(X0,X1,X2) ),
inference(cnf_transformation,[],[f330]) ).
tcf(c_59846,plain,
! [X0: $i,X1: $i,X2: $i] :
( aElementOf0(X0,X1)
| ~ aSet0(X1)
| ~ aElement0(X2)
| ~ aElementOf0(X0,sdtmndt0(X1,X2)) ),
inference(superposition,[status(thm)],[c_2260,c_85]) ).
tcf(c_88068,plain,
( aElementOf0(sK41,sdtlpdtrp0(xN,sK14(sK40)))
| ( sz00 = sK40 )
| ~ aSet0(sdtlpdtrp0(xN,sK14(sK40)))
| ~ aElement0(szmzizndt0(sdtlpdtrp0(xN,sK14(sK40))))
| ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,sK14(sK40)),szmzizndt0(sdtlpdtrp0(xN,sK14(sK40))))) ),
inference(superposition,[status(thm)],[c_61267,c_59846]) ).
tcf(c_91789,plain,
( ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,sK14(sK40)),szmzizndt0(sdtlpdtrp0(xN,sK14(sK40)))))
| ( sz00 = sK40 ) ),
inference(global_subsumption_just,[status(thm)],[c_91770,c_30715,c_42860,c_43005,c_43728,c_43878,c_71032,c_88068]) ).
tcf(c_91790,plain,
( ( sz00 = sK40 )
| ~ aSet0(sdtmndt0(sdtlpdtrp0(xN,sK14(sK40)),szmzizndt0(sdtlpdtrp0(xN,sK14(sK40))))) ),
inference(renaming,[status(thm)],[c_91789]) ).
tcf(c_91791,plain,
( ( sz00 = sK40 )
| ~ sP9(sK14(sK40)) ),
inference(superposition,[status(thm)],[c_251,c_91790]) ).
tcf(c_91801,plain,
sz00 = sK40,
inference(global_subsumption_just,[status(thm)],[c_91791,c_274,c_36695,c_91791]) ).
tcf(c_91877,plain,
( ~ aElementOf0(sK41,szNzAzT0)
| ~ isCountable0(sdtlpdtrp0(xN,sK40))
| ~ aSet0(sdtlpdtrp0(xN,sz00)) ),
inference(superposition,[status(thm)],[c_91801,c_267]) ).
tcf(c_91878,plain,
( ~ isCountable0(sdtlpdtrp0(xN,sK40))
| ~ aSubsetOf0(sdtlpdtrp0(xN,sz00),szNzAzT0) ),
inference(superposition,[status(thm)],[c_91801,c_269]) ).
tcf(c_92010,plain,
( ~ aSubsetOf0(xS,szNzAzT0)
| ~ isCountable0(sdtlpdtrp0(xN,sK40)) ),
inference(superposition,[status(thm)],[c_263,c_91878]) ).
tcf(c_92011,plain,
~ isCountable0(sdtlpdtrp0(xN,sK40)),
inference(global_subsumption_just,[status(thm)],[c_91877,c_197,c_92010]) ).
tcf(c_92013,plain,
~ isCountable0(sdtlpdtrp0(xN,sz00)),
inference(superposition,[status(thm)],[c_91801,c_92011]) ).
tcf(c_92014,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_92013,c_31672,c_263,c_198]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM569+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.11/0.38 % Computer : n019.cluster.edu
% 0.11/0.38 % Model : x86_64 x86_64
% 0.11/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.38 % Memory : 8046.5625MB
% 0.11/0.38 % OS : Linux 6.8.0-71-generic
% 0.11/0.38 % CPULimit : 300
% 0.11/0.38 % WCLimit : 300
% 0.11/0.38 % DateTime : Thu Sep 24 04:41:04 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.11/0.42 Running first-order theorem proving
% 0.11/0.42 Running: /export/starexec/sandbox2/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/0.43
% 0.11/0.43 % ======== iProver multi-core TPTP/SMT =========
% 0.11/0.43
% 0.11/0.43 % Detected problem language: tptp
% 0.11/0.45 % Proving...
% 80.58/18.53 % SZS status Started for theBenchmark.p
% 80.58/18.53 % SZS status Theorem for theBenchmark.p
% 80.58/18.53
% 80.58/18.53 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 80.58/18.53
% 80.58/18.53 % ------ iProver source info
% 80.58/18.53
% 80.58/18.53 % git: date: 2026-07-19 20:42:38 +0200
% 80.58/18.53 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 80.58/18.53 % git: non_committed_changes: false
% 80.58/18.53
% 80.58/18.53 % ------ Parsing...
% 80.58/18.53 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 80.58/18.53
% 80.58/18.53 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe:1:0s pe:2:0s pe:4:0s pe_e sup_sim: 0 sf_s rm: 2 0s sf_e pe_s pe_e %
% 80.58/18.53
% 80.58/18.53 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 80.58/18.53
% 80.58/18.53 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 80.58/18.53 % ------ Proving...
% 80.58/18.53 % ------ Problem Properties
% 80.58/18.53
% 80.58/18.53 %
% 80.58/18.53 % clauses 221
% 80.58/18.53 % conjectures 4
% 80.58/18.53 % EPR 44
% 80.58/18.53 % Horn 170
% 80.58/18.53 % unary 26
% 80.58/18.53 % binary 44
% 80.58/18.53 % lits 758
% 80.58/18.53 % lits eq 107
% 80.58/18.53 % fd_pure 0
% 80.58/18.53 % fd_pseudo 0
% 80.58/18.53 % fd_cond 10
% 80.58/18.53 % fd_pseudo_cond 30
% 80.58/18.53 % AC symbols 0
% 80.58/18.53
% 80.58/18.53 % ------ Input Options Time Limit: Unbounded
% 80.58/18.53
% 80.58/18.53
% 80.58/18.53 % ------
% 80.58/18.53 % Current options:
% 80.58/18.53 % ------
% 80.58/18.53
% 80.58/18.53
% 80.58/18.53 %
% 80.58/18.53
% 80.58/18.53 % ------ Proving...
% 80.58/18.53 %
% 80.58/18.53
% 80.58/18.53 % SZS status Theorem for theBenchmark.p
% 80.58/18.53
% 80.58/18.53 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 80.58/18.54
% 80.58/18.54
%------------------------------------------------------------------------------